internal DatatypeSort(Context ctx, Symbol name, Constructor[] constructors)
: base(ctx, Native.Z3_mk_datatype(ctx.nCtx, name.NativeObject, (uint)constructors.Length, ArrayToNative(constructors)))
{
Contract.Requires(ctx != null);
Contract.Requires(name != null);
Contract.Requires(constructors != null);
}
internal ConstructorList(Context ctx, Constructor[] constructors)
: base(ctx)
{
Contract.Requires(ctx != null);
Contract.Requires(constructors != null);
NativeObject = Native.Z3_mk_constructor_list(Context.nCtx, (uint)constructors.Length, Constructor.ArrayToNative(constructors));
}
/// <summary>
/// Create mutually recursive data-types.
/// </summary>
/// <param name="names"></param>
/// <param name="c"></param>
/// <returns></returns>
public DatatypeSort[] MkDatatypeSorts(string[] names, Constructor[][] c)
{
Contract.Requires(names != null);
Contract.Requires(c != null);
Contract.Requires(names.Length == c.Length);
Contract.Requires(Contract.ForAll(0, c.Length, j => c[j] != null));
Contract.Requires(Contract.ForAll(names, name => name != null));
Contract.Ensures(Contract.Result<DatatypeSort[]>() != null);
return MkDatatypeSorts(MkSymbols(names), c);
}
/// <summary>
/// Create mutually recursive datatypes.
/// </summary>
/// <param name="names">names of datatype sorts</param>
/// <param name="c">list of constructors, one list per sort.</param>
public DatatypeSort[] MkDatatypeSorts(Symbol[] names, Constructor[][] c)
{
Contract.Requires(names != null);
Contract.Requires(c != null);
Contract.Requires(names.Length == c.Length);
Contract.Requires(Contract.ForAll(0, c.Length, j => c[j] != null));
Contract.Requires(Contract.ForAll(names, name => name != null));
Contract.Ensures(Contract.Result<DatatypeSort[]>() != null);
CheckContextMatch(names);
uint n = (uint)names.Length;
ConstructorList[] cla = new ConstructorList[n];
IntPtr[] n_constr = new IntPtr[n];
for (uint i = 0; i < n; i++)
{
Constructor[] constructor = c[i];
Contract.Assume(Contract.ForAll(constructor, arr => arr != null), "Clousot does not support yet quantified formula on multidimensional arrays");
CheckContextMatch(constructor);
cla[i] = new ConstructorList(this, constructor);
n_constr[i] = cla[i].NativeObject;
}
IntPtr[] n_res = new IntPtr[n];
Native.Z3_mk_datatypes(nCtx, n, Symbol.ArrayToNative(names), n_res, n_constr);
DatatypeSort[] res = new DatatypeSort[n];
for (uint i = 0; i < n; i++)
res[i] = new DatatypeSort(this, n_res[i]);
return res;
}
/// <summary>
/// Create a new datatype sort.
/// </summary>
public DatatypeSort MkDatatypeSort(string name, Constructor[] constructors)
{
Contract.Requires(constructors != null);
Contract.Requires(Contract.ForAll(constructors, c => c != null));
Contract.Ensures(Contract.Result<DatatypeSort>() != null);
CheckContextMatch(constructors);
return new DatatypeSort(this, MkSymbol(name), constructors);
}
/// <summary>
/// Create a forest of trees.
/// </summary>
/// <remarks>
/// forest ::= nil | cons(tree, forest)
/// tree ::= nil | cons(forest, forest)
/// </remarks>
public static void ForestExample(Context ctx)
{
Console.WriteLine("ForestExample");
Sort tree, forest;
FuncDecl nil1_decl, is_nil1_decl, cons1_decl, is_cons1_decl, car1_decl, cdr1_decl;
FuncDecl nil2_decl, is_nil2_decl, cons2_decl, is_cons2_decl, car2_decl, cdr2_decl;
Expr nil1, nil2, t1, t2, t3, t4, f1, f2, f3, l1, l2, x, y, u, v;
//
// Declare the names of the accessors for cons.
// Then declare the sorts of the accessors.
// For this example, all sorts refer to the new types 'forest' and 'tree'
// being declared, so we pass in null for both sorts1 and sorts2.
// On the other hand, the sort_refs arrays contain the indices of the
// two new sorts being declared. The first element in sort1_refs
// points to 'tree', which has index 1, the second element in sort1_refs array
// points to 'forest', which has index 0.
//
Symbol[] head_tail1 = new Symbol[] { ctx.MkSymbol("head"), ctx.MkSymbol("tail") };
Sort[] sorts1 = new Sort[] { null, null };
uint[] sort1_refs = new uint[] { 1, 0 }; // the first item points to a tree, the second to a forest
Symbol[] head_tail2 = new Symbol[] { ctx.MkSymbol("car"), ctx.MkSymbol("cdr") };
Sort[] sorts2 = new Sort[] { null, null };
uint[] sort2_refs = new uint[] { 0, 0 }; // both items point to the forest datatype.
Constructor nil1_con, cons1_con, nil2_con, cons2_con;
Constructor[] constructors1 = new Constructor[2], constructors2 = new Constructor[2];
Symbol[] sort_names = { ctx.MkSymbol("forest"), ctx.MkSymbol("tree") };
/* build a forest */
nil1_con = ctx.MkConstructor(ctx.MkSymbol("nil"), ctx.MkSymbol("is_nil"), null, null, null);
cons1_con = ctx.MkConstructor(ctx.MkSymbol("cons1"), ctx.MkSymbol("is_cons1"), head_tail1, sorts1, sort1_refs);
constructors1[0] = nil1_con;
constructors1[1] = cons1_con;
/* build a tree */
nil2_con = ctx.MkConstructor(ctx.MkSymbol("nil2"), ctx.MkSymbol("is_nil2"), null, null, null);
cons2_con = ctx.MkConstructor(ctx.MkSymbol("cons2"), ctx.MkSymbol("is_cons2"), head_tail2, sorts2, sort2_refs);
constructors2[0] = nil2_con;
constructors2[1] = cons2_con;
Constructor[][] clists = new Constructor[][] { constructors1, constructors2 };
Sort[] sorts = ctx.MkDatatypeSorts(sort_names, clists);
forest = sorts[0];
tree = sorts[1];
//
// Now that the datatype has been created.
// Query the constructors for the constructor
// functions, testers, and field accessors.
//
nil1_decl = nil1_con.ConstructorDecl;
is_nil1_decl = nil1_con.TesterDecl;
cons1_decl = cons1_con.ConstructorDecl;
is_cons1_decl = cons1_con.TesterDecl;
FuncDecl[] cons1_accessors = cons1_con.AccessorDecls;
car1_decl = cons1_accessors[0];
cdr1_decl = cons1_accessors[1];
nil2_decl = nil2_con.ConstructorDecl;
is_nil2_decl = nil2_con.TesterDecl;
cons2_decl = cons2_con.ConstructorDecl;
is_cons2_decl = cons2_con.TesterDecl;
FuncDecl[] cons2_accessors = cons2_con.AccessorDecls;
car2_decl = cons2_accessors[0];
cdr2_decl = cons2_accessors[1];
nil1 = ctx.MkConst(nil1_decl);
nil2 = ctx.MkConst(nil2_decl);
f1 = ctx.MkApp(cons1_decl, nil2, nil1);
t1 = ctx.MkApp(cons2_decl, nil1, nil1);
t2 = ctx.MkApp(cons2_decl, f1, nil1);
t3 = ctx.MkApp(cons2_decl, f1, f1);
t4 = ctx.MkApp(cons2_decl, nil1, f1);
f2 = ctx.MkApp(cons1_decl, t1, nil1);
f3 = ctx.MkApp(cons1_decl, t1, f1);
/* nil != cons(nil,nil) */
Prove(ctx, ctx.MkNot(ctx.MkEq(nil1, f1)));
Prove(ctx, ctx.MkNot(ctx.MkEq(nil2, t1)));
/* cons(x,u) = cons(x, v) => u = v */
u = ctx.MkConst("u", forest);
v = ctx.MkConst("v", forest);
x = ctx.MkConst("x", tree);
y = ctx.MkConst("y", tree);
l1 = ctx.MkApp(cons1_decl, x, u);
l2 = ctx.MkApp(cons1_decl, y, v);
Prove(ctx, ctx.MkImplies(ctx.MkEq(l1, l2), ctx.MkEq(u, v)));
Prove(ctx, ctx.MkImplies(ctx.MkEq(l1, l2), ctx.MkEq(x, y)));
/* is_nil(u) or is_cons(u) */
Prove(ctx, ctx.MkOr((BoolExpr)ctx.MkApp(is_nil1_decl, u),
(BoolExpr)ctx.MkApp(is_cons1_decl, u)));
/* occurs check u != cons(x,u) */
Prove(ctx, ctx.MkNot(ctx.MkEq(u, l1)));
}
/// <summary>
/// Create a binary tree datatype.
/// </summary>
public static void TreeExample(Context ctx)
{
Console.WriteLine("TreeExample");
Sort cell;
FuncDecl nil_decl, is_nil_decl, cons_decl, is_cons_decl, car_decl, cdr_decl;
Expr nil, l1, l2, x, y, u, v;
BoolExpr fml, fml1;
string[] head_tail = new string[] { "car", "cdr" };
Sort[] sorts = new Sort[] { null, null };
uint[] sort_refs = new uint[] { 0, 0 };
Constructor nil_con, cons_con;
nil_con = ctx.MkConstructor("nil", "is_nil", null, null, null);
cons_con = ctx.MkConstructor("cons", "is_cons", head_tail, sorts, sort_refs);
Constructor[] constructors = new Constructor[] { nil_con, cons_con };
cell = ctx.MkDatatypeSort("cell", constructors);
nil_decl = nil_con.ConstructorDecl;
is_nil_decl = nil_con.TesterDecl;
cons_decl = cons_con.ConstructorDecl;
is_cons_decl = cons_con.TesterDecl;
FuncDecl[] cons_accessors = cons_con.AccessorDecls;
car_decl = cons_accessors[0];
cdr_decl = cons_accessors[1];
nil = ctx.MkConst(nil_decl);
l1 = ctx.MkApp(cons_decl, nil, nil);
l2 = ctx.MkApp(cons_decl, l1, nil);
/* nil != cons(nil, nil) */
Prove(ctx, ctx.MkNot(ctx.MkEq(nil, l1)));
/* cons(x,u) = cons(x, v) => u = v */
u = ctx.MkConst("u", cell);
v = ctx.MkConst("v", cell);
x = ctx.MkConst("x", cell);
y = ctx.MkConst("y", cell);
l1 = ctx.MkApp(cons_decl, x, u);
l2 = ctx.MkApp(cons_decl, y, v);
Prove(ctx, ctx.MkImplies(ctx.MkEq(l1, l2), ctx.MkEq(u, v)));
Prove(ctx, ctx.MkImplies(ctx.MkEq(l1, l2), ctx.MkEq(x, y)));
/* is_nil(u) or is_cons(u) */
Prove(ctx, ctx.MkOr((BoolExpr)ctx.MkApp(is_nil_decl, u), (BoolExpr)ctx.MkApp(is_cons_decl, u)));
/* occurs check u != cons(x,u) */
Prove(ctx, ctx.MkNot(ctx.MkEq(u, l1)));
/* destructors: is_cons(u) => u = cons(car(u),cdr(u)) */
fml1 = ctx.MkEq(u, ctx.MkApp(cons_decl, ctx.MkApp(car_decl, u), ctx.MkApp(cdr_decl, u)));
fml = ctx.MkImplies((BoolExpr)ctx.MkApp(is_cons_decl, u), fml1);
Console.WriteLine("Formula {0}", fml);
Prove(ctx, fml);
Disprove(ctx, fml1);
}
internal ConstructorList(Context ctx, Constructor[] constructors)
: base(ctx)
{
Contract.Requires(ctx != null);
Contract.Requires(constructors != null);
NativeObject = Native.Z3_mk_constructor_list(Context.nCtx, (uint)constructors.Length, Constructor.ArrayToNative(constructors));
}
